$\dfrac{d}{dx}[3\text{ln}(x)-12\text{sin}(x)]=$
Solution: Recall that ${\dfrac{d}{dx}[\text{ln}(x)]=\dfrac1x}$ and ${\dfrac{d}{dx}[\text{sin}(x)]=\text{cos}(x)}$. $\begin{aligned} &\phantom{=}\dfrac{d}{dx}[3\text{ln}(x)-12\text{sin}(x)] \\\\ &=3{\dfrac{d}{dx}[\text{ln}(x)]}-12{\dfrac{d}{dx}[\text{sin}(x)]} \\\\ &=3\cdot{\dfrac1x}-12\cdot{\text{cos}(x)} \\\\ &=\dfrac3x-12\text{cos}(x) \end{aligned}$ In conclusion, $\dfrac{d}{dx}[3\text{ln}(x)-12\text{sin}(x)]=\dfrac3x-12\text{cos}(x)$